Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets ...

The theory has an axiom of unrestricted pairwise union, however, and unrestricted complements. An interpretation of the axioms in a set theory similar to Zermelo-Fraenkel set theory with global choice ...

The fact that symmetric functions undergo sharp thresholds is important in the study of random graphs and constraint satisfaction problems as well as in social choice. In this paper we prove sharp ...